Stability domain of the second‐order discrete oscillatory system with parametric excitation

Toshiyuki Tanaka, Chikara Sato

Research output: Contribution to journalArticle

Abstract

This paper presents a quantitative discussion on the stability of the second‐order periodic difference equation, which characterizes the discrete periodic time‐varying system. the periodic parameter discrete system, which corresponds to Mathieu's equation in the continuous system, is represented by a second‐order linear difference equation with a small parameter ε in the varying term. the parameter ε plays an important role in the determination of the stability. By applying McLachlan's method, the expression for the boundary between the stability and the instability can be determined analytically with regard to the parameters contained in the equation. For the case where the periodic parameter of the difference equation is represented as a sum of two even functions, the boundary between stability and instability is determined. the stability can be analyzed in a similar way for the case where the periodic parameter is represented as a sum of N even functions in Fourier series.

Original languageEnglish
Pages (from-to)109-116
Number of pages8
JournalElectronics and Communications in Japan (Part III: Fundamental Electronic Science)
Volume72
Issue number2
DOIs
Publication statusPublished - 1989

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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